Problem: Simplify the following expression: $x = \dfrac{42k^3 + 70k^2}{91k^2}$ You can assume $k \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $42k^3 + 70k^2 = (2\cdot3\cdot7 \cdot k \cdot k \cdot k) + (2\cdot5\cdot7 \cdot k \cdot k)$ The denominator can be factored: $91k^2 = (7\cdot13 \cdot k \cdot k)$ The greatest common factor of all the terms is $7k^2$ Factoring out $7k^2$ gives us: $x = \dfrac{(7k^2)(6k + 10)}{(7k^2)(13)}$ Dividing both the numerator and denominator by $7k^2$ gives: $x = \dfrac{6k + 10}{13}$